Technical Report Extended Figures

Document Introduction

This will instead include a document summary section, a project summary, and links to other important documentation.

Model code example

Show the code

## RTMB dat and par setup ####
# Dat
dat <- list(srdat = srdat,
            WAbase = WAbase,
            WAin = WAin,
            lineWA =  seq(min(WAbase$logWAshifted), 
                          max(WAbase$logWAshifted), 0.1), # Not added to NLL
            mean_logWA = mean_logWA,
            logRS = log(srdat$Rec) - log(srdat$Sp),
            prioronly = 0) # 0-run with data, 1-prior prediction mode

# External vectors
N_Stk <- max(srdat$Stocknumber + 1)
N_Obs <- nrow(srdat)
stk = srdat$Stocknumber + 1
lhdiston <- T 
bias.cor <- F 

# Parameters/Initial values
par <- list(b0 = c(10, 0), # Initial values for WA regression intercepts
            bWA = c(0, 0), # Inital values for WA regression slopes
            logSREP_re = numeric(N_Stk), # Zeroes
            logAlpha0 = 0.6,
            logAlpha_re = numeric(nrow(dat$WAbase)), # Zeroes
            tauobs = 0.01 + numeric(N_Stk), # Constrained positive
            logSREP_sd = 1, 
            logAlpha_sd = 1
)
if (lhdiston) {
  par$logAlpha02 <- 0
}

f_srep <- function(par){
  getAll(dat, par)
  
  N_Stk = max(srdat$Stocknumber + 1) # number of stocks
  stk = srdat$Stocknumber + 1 # vector of stocknumbers
  N_Obs = nrow(srdat) # number of observations
  N_Pred = nrow(WAin) # number of predicted watershed areas
  
  S = srdat$Sp
  type = lifehist$lh
  type_tar = as.numeric(WAin$lh) 

  SREP <- numeric(N_Stk)
  # logE_pred <- numeric(N_Stk)
  logSREP <- numeric(N_Stk)
  logAlpha <- numeric(N_Stk)
  
  logRS_pred <- numeric(N_Obs) 

  SREP_tar <- numeric(N_Pred)
  logSREP_tar <- numeric(N_Pred)
  logAlpha_tar <- numeric(N_Pred)
  
  # Simulated line vectors
  line <- length(lineWA)
  logSREP_line_stream <- numeric(line)
  SREP_line_stream <- numeric(line)
  logSREP_line_ocean <- numeric(line)
  SREP_line_ocean <- numeric(line)
  
  if (bias.cor) {
    biaslogSREP <- -0.5*logSREP_sd^2
    biaslogAlpha <- -0.5*logAlpha_sd^2
    biaslogRS <- -0.5*(sqrt(1/tauobs))^2
  } else {
    biaslogSREP <- 0
    biaslogAlpha <- 0
    biaslogRS <- numeric(N_Stk)
  }
  
  nll <- 0 # Begin negative log-likelihood
  
  nll <- nll - sum(dnorm(b0[1], 10, sd = 31.6, log = TRUE)) # Prior
  nll <- nll - sum(dnorm(b0[2], 0, sd = 31.6, log = TRUE)) # Prior
  nll <- nll - sum(dnorm(bWA[1], 0, sd = 31.6, log = TRUE)) # Prior
  nll <- nll - sum(dnorm(bWA[2], 0, sd = 31.6, log = TRUE)) # Prior
  
  nll <- nll - sum(dnorm(logAlpha0, 0.6, sd = 0.45, log = TRUE)) # Prior (rM)
  if(lhdiston) nll <- nll - sum(dnorm(logAlpha02, 0, sd = 31.6, log = TRUE)) # Prior (rD)
  
  ## Second level of hierarchy - Ricker parameters:
  for (i in 1:N_Stk){
    nll <- nll - dnorm(logSREP_re[i], 0, sd = 1, log = TRUE) 
    
    logSREP[i] <- b0[1] + b0[2]*type[i] + (bWA[1] + bWA[2]*type[i]) * WAbase$logWAshifted[i] + logSREP_re[i]*logSREP_sd + biaslogSREP
    SREP[i] <- exp(logSREP[i])
    
    nll <- nll - dnorm(logAlpha_re[i], 0, sd = 1, log = TRUE) 

    if(lhdiston) logAlpha[i] <- logAlpha0 + logAlpha02*type[i] + logAlpha_re[i]*logAlpha_sd + biaslogAlpha
    else logAlpha[i] <- logAlpha0 + logAlpha_re[i]*logAlpha_sd + biaslogAlpha

    nll <- nll - dgamma(tauobs[i], shape = 0.0001, scale = 1/0.0001, log = TRUE)
  }

  ## First level of hierarchy: Ricker model:
  for (i in 1:N_Obs){
    logRS_pred[i] <- logAlpha[stk[i]]*(1 - S[i]/SREP[stk[i]]) + biaslogRS[stk[i]]

    if(!prioronly){
      nll <- nll - dnorm(logRS[i], logRS_pred[i], sd = sqrt(1/tauobs[stk[i]]), log = TRUE)
    } 
      
  }
  
  ## Calculate SMSY for Synoptic set - for plotting
  SMSY_r = numeric(nrow(WAbase))
  BETA_r = numeric(nrow(WAbase))
  
  for (i in 1:N_Stk){
    BETA_r[i] <- logAlpha[i] / SREP[i]
    SMSY_r[i] <- (1 - LambertW0(exp(1 - logAlpha[i]))) / BETA_r[i]
  }

  ## PREDICTIONS
  BETA = numeric(nrow(WAin))
  SMSY = numeric(nrow(WAin))
  SGEN = numeric(nrow(WAin))

  for (i in 1:N_Pred){
    if(lhdiston) logAlpha_tar[i] <- logAlpha0 + logAlpha02*type_tar[i] + biaslogAlpha 
    else logAlpha_tar[i] <- logAlpha0 + biaslogAlpha

    logSREP_tar[i] <- b0[1] + b0[2]*type_tar[i] + (bWA[1] + bWA[2]*type_tar[i])*WAin$logWAshifted_t[i] + biaslogSREP
    SREP_tar[i] <- exp(logSREP_tar[i])
    
    # Predict BETA
    BETA[i] <- logAlpha_tar[i]/SREP_tar[i]
    # Predict SMSY
    SMSY[i] <- (1-LambertW0(exp(1-logAlpha_tar[i])))/BETA[i]
    # Predict SGEN
    SGEN[i] <- -1/BETA[i]*LambertW0(-BETA[i]*SMSY[i]/(exp(logAlpha_tar[i])))
  }
  
  # Create predictions on an simulated line
  for (i in 1:line){
    logSREP_line_ocean[i] <- b0[1] + b0[2] + (bWA[1] + bWA[2])*lineWA[i] + biaslogSREP # DATA - not in likelihood
    SREP_line_ocean[i] <- exp(logSREP_line_ocean[i])
    
    logSREP_line_stream[i] <- b0[1] + (bWA[1])*lineWA[i] + biaslogSREP # DATA - not in likelihood
    SREP_line_stream[i] <- exp(logSREP_line_stream[i])
  }
  
  ## ADREPORT - internal values (synoptic specific/Ricker)  
  REPORT(b0) # Testing simulate()
  REPORT(bWA) # Testing simulate()

  REPORT(logRS_pred)
  
  alpha <- exp(logAlpha)
  # REPORT(logRS) # logRS for all 501 data points
  REPORT(logSREP_re)
  REPORT(logSREP_sd)
  REPORT(SREP) # E (Srep) for all synoptic data set rivers (25)
  REPORT(logSREP)
  REPORT(logAlpha) # model logAlpha (25)
  REPORT(logAlpha0)
  REPORT(logAlpha02)
  REPORT(logAlpha_re) # random effect parameter for resampling
  REPORT(logAlpha_sd)
  REPORT(alpha)
  REPORT(SMSY_r)
  REPORT(BETA_r)
  REPORT(tauobs) # Necessary to add back in observation error?

  alpha_tar <- exp(logAlpha_tar)
  
  REPORT(SREP_tar)
  REPORT(logSREP_tar)
  REPORT(logAlpha_tar)
  REPORT(alpha_tar)
  
  REPORT(BETA)
  REPORT(SMSY)
  REPORT(SGEN)
  
  # Simulated line values for plotting
  REPORT(SREP_line_stream) 
  REPORT(logSREP_line_stream) 
  REPORT(SREP_line_ocean) 
  REPORT(logSREP_line_ocean)
  
  nll # output of negative log-likelihood
}

Extended Results Section: Figures and Tables

1. Model Parameter Trace Plots

b0

b0[1]

b0[2]

bWA

bWA[1]

bWA[2]

logAlpha_re

logAlpha_re[1]

logAlpha_re[2]

logAlpha_re[3]

logAlpha_re[4]

logAlpha_re[5]

logAlpha_re[6]

logAlpha_re[7]

logAlpha_re[8]

logAlpha_re[9]

logAlpha_re[10]

logAlpha_re[11]

logAlpha_re[12]

logAlpha_re[13]

logAlpha_re[14]

logAlpha_re[15]

logAlpha_re[16]

logAlpha_re[17]

logAlpha_re[18]

logAlpha_re[19]

logAlpha_re[20]

logAlpha_re[21]

logAlpha_re[22]

logAlpha_re[23]

logAlpha_re[24]

logAlpha_re[25]

logAlpha_sd

logAlpha_sd

logAlpha0

logAlpha0

logAlpha02

logAlpha02

logSREP_re

logSREP_re[1]

logSREP_re[2]

logSREP_re[3]

logSREP_re[4]

logSREP_re[5]

logSREP_re[6]

logSREP_re[7]

logSREP_re[8]

logSREP_re[9]

logSREP_re[10]

logSREP_re[11]

logSREP_re[12]

logSREP_re[13]

logSREP_re[14]

logSREP_re[15]

logSREP_re[16]

logSREP_re[17]

logSREP_re[18]

logSREP_re[19]

logSREP_re[20]

logSREP_re[21]

logSREP_re[22]

logSREP_re[23]

logSREP_re[24]

logSREP_re[25]

logSREP_sd

logSREP_sd

lp__

lp__

tauobs

tauobs[1]

tauobs[2]

tauobs[3]

tauobs[4]

tauobs[5]

tauobs[6]

tauobs[7]

tauobs[8]

tauobs[9]

tauobs[10]

tauobs[11]

tauobs[12]

tauobs[13]

tauobs[14]

tauobs[15]

tauobs[16]

tauobs[17]

tauobs[18]

tauobs[19]

tauobs[20]

tauobs[21]

tauobs[22]

tauobs[23]

tauobs[24]

tauobs[25]

2. Model Parameter Autocorrelation Plots

b0

b0[1]

b0[2]

bWA

bWA[1]

bWA[2]

logAlpha_re

logAlpha_re[1]

logAlpha_re[2]

logAlpha_re[3]

logAlpha_re[4]

logAlpha_re[5]

logAlpha_re[6]

logAlpha_re[7]

logAlpha_re[8]

logAlpha_re[9]

logAlpha_re[10]

logAlpha_re[11]

logAlpha_re[12]

logAlpha_re[13]

logAlpha_re[14]

logAlpha_re[15]

logAlpha_re[16]

logAlpha_re[17]

logAlpha_re[18]

logAlpha_re[19]

logAlpha_re[20]

logAlpha_re[21]

logAlpha_re[22]

logAlpha_re[23]

logAlpha_re[24]

logAlpha_re[25]

logAlpha_sd

logAlpha_sd

logAlpha0

logAlpha0

logAlpha02

logAlpha02

logSREP_re

logSREP_re[1]

logSREP_re[2]

logSREP_re[3]

logSREP_re[4]

logSREP_re[5]

logSREP_re[6]

logSREP_re[7]

logSREP_re[8]

logSREP_re[9]

logSREP_re[10]

logSREP_re[11]

logSREP_re[12]

logSREP_re[13]

logSREP_re[14]

logSREP_re[15]

logSREP_re[16]

logSREP_re[17]

logSREP_re[18]

logSREP_re[19]

logSREP_re[20]

logSREP_re[21]

logSREP_re[22]

logSREP_re[23]

logSREP_re[24]

logSREP_re[25]

logSREP_sd

logSREP_sd

lp__

lp__

tauobs

tauobs[1]

tauobs[2]

tauobs[3]

tauobs[4]

tauobs[5]

tauobs[6]

tauobs[7]

tauobs[8]

tauobs[9]

tauobs[10]

tauobs[11]

tauobs[12]

tauobs[13]

tauobs[14]

tauobs[15]

tauobs[16]

tauobs[17]

tauobs[18]

tauobs[19]

tauobs[20]

tauobs[21]

tauobs[22]

tauobs[23]

tauobs[24]

tauobs[25]

3. Model Parameter Pairs Plots

Show figure: Pairs Plots

4. Convergence Diagnostic Statistics Table

Geweke Statistics

Show table

Parameter	Chain1	Chain2	Chain3	Chain4
b0[1]	-1.478	0.678	0.526	-0.176
b0[2]	2.562	-0.712	-0.572	-0.429
bWA[1]	-0.801	-2.093	-0.692	0.380
bWA[2]	0.839	-0.174	0.621	-0.302
logSREP_re[1]	-0.818	1.114	0.657	0.573
logSREP_re[2]	1.066	0.488	0.653	0.050
logSREP_re[3]	1.860	-0.048	1.489	-0.338
logSREP_re[4]	0.767	-1.123	1.806	0.629
logSREP_re[5]	0.306	-0.671	-0.744	-0.018
logSREP_re[6]	0.982	-1.024	-0.916	0.026
logSREP_re[7]	0.417	-1.477	-1.103	0.610
logSREP_re[8]	-0.196	-0.085	-1.257	0.724
logSREP_re[9]	0.388	-1.350	-0.286	0.573
logSREP_re[10]	-1.321	1.816	0.654	1.200
logSREP_re[11]	-0.518	-0.574	0.020	0.816
logSREP_re[12]	-0.617	-1.143	0.052	-0.014
logSREP_re[13]	-1.825	0.620	-0.257	0.693
logSREP_re[14]	-0.787	0.104	0.793	0.414
logSREP_re[15]	0.897	-1.892	-0.564	0.376
logSREP_re[16]	2.517	-0.231	-0.177	0.510
logSREP_re[17]	1.308	0.643	0.496	-0.651
logSREP_re[18]	1.948	-0.457	0.574	0.874
logSREP_re[19]	0.772	0.291	1.259	-0.053
logSREP_re[20]	-1.245	1.202	-1.241	-0.873
logSREP_re[21]	-0.043	-0.605	-0.307	1.297
logSREP_re[22]	-1.431	1.576	1.504	1.099
logSREP_re[23]	0.455	0.880	-0.183	-0.187
logSREP_re[24]	-1.952	-0.265	-1.027	-0.456
logSREP_re[25]	-1.964	0.488	1.715	0.954
logAlpha0	-0.735	-1.040	-1.453	-0.998
logAlpha_re[1]	0.496	-1.772	0.447	-0.896
logAlpha_re[2]	-1.449	-1.607	-0.566	0.416
logAlpha_re[3]	-0.659	-0.046	2.075	0.385
logAlpha_re[4]	1.020	0.848	-1.472	-0.252
logAlpha_re[5]	2.105	1.101	3.849	1.352
logAlpha_re[6]	0.097	-0.491	1.364	0.508
logAlpha_re[7]	-0.099	-0.371	0.169	-0.169
logAlpha_re[8]	0.017	-1.036	1.216	-0.406
logAlpha_re[9]	2.250	1.114	1.575	-0.903
logAlpha_re[10]	1.263	-1.551	-1.220	0.704
logAlpha_re[11]	2.610	0.993	-0.120	-0.493
logAlpha_re[12]	0.767	0.492	-0.501	0.573
logAlpha_re[13]	0.125	0.646	0.694	0.712
logAlpha_re[14]	0.210	0.193	0.291	0.395
logAlpha_re[15]	0.577	1.760	0.516	1.587
logAlpha_re[16]	0.077	-0.221	-1.000	-1.796
logAlpha_re[17]	2.545	1.574	1.468	0.702
logAlpha_re[18]	0.738	0.426	-0.741	-0.436
logAlpha_re[19]	1.292	0.116	1.032	0.058
logAlpha_re[20]	-0.365	-1.227	0.265	0.080
logAlpha_re[21]	0.688	1.061	0.501	-0.636
logAlpha_re[22]	0.566	-0.771	-1.244	0.331
logAlpha_re[23]	-0.168	0.017	0.738	0.945
logAlpha_re[24]	0.037	-0.013	-0.829	0.204
logAlpha_re[25]	0.616	0.099	0.670	-0.337
tauobs[1]	-0.205	1.222	0.010	-0.569
tauobs[2]	1.568	-0.863	0.456	-0.876
tauobs[3]	-1.845	0.568	0.004	0.629
tauobs[4]	0.277	1.259	-1.279	0.874
tauobs[5]	1.070	0.863	-0.809	-0.430
tauobs[6]	-0.735	-0.466	0.022	0.426
tauobs[7]	-2.194	1.267	2.178	-0.725
tauobs[8]	-0.242	-1.496	-0.593	-0.645
tauobs[9]	1.533	0.561	-0.382	-0.983
tauobs[10]	0.795	-1.397	1.576	0.233
tauobs[11]	-1.035	1.485	-1.533	-1.563
tauobs[12]	0.074	0.298	-2.962	0.983
tauobs[13]	-1.569	-0.592	-0.015	0.651
tauobs[14]	-1.562	0.584	0.871	1.600
tauobs[15]	1.728	1.924	0.091	0.785
tauobs[16]	-0.599	0.741	-0.900	0.641
tauobs[17]	1.460	0.869	0.859	-0.110
tauobs[18]	-0.290	-0.411	-0.026	-1.581
tauobs[19]	1.236	-0.732	1.602	-1.161
tauobs[20]	1.167	1.049	0.405	0.951
tauobs[21]	-1.089	0.784	0.415	0.632
tauobs[22]	0.958	-1.053	-1.097	-0.504
tauobs[23]	-0.362	-0.951	-0.283	-0.944
tauobs[24]	-0.168	1.219	0.455	-1.063
tauobs[25]	0.054	1.521	-0.086	-1.065
logSREP_sd	-0.910	-0.970	0.165	-0.171
logAlpha_sd	1.016	2.006	1.245	0.624
logAlpha02	-0.493	0.573	1.011	0.186
lp__	-0.928	1.020	0.149	0.491

Show Chain 1

Show Chain 2

Show Chain 3

Show Chain 4

Heidelberg etc. Statistics

Show Chain 1

	stest	start	pvalue	htest	mean	halfwidth
b0[1]	1	1	0.256	1	8.941	0.010
b0[2]	1	251	0.458	1	1.042	0.015
bWA[1]	1	1	0.394	1	0.680	0.004
bWA[2]	1	1	0.442	1	0.281	0.010
logSREP_re[1]	1	1	0.363	1	0.758	0.043
logSREP_re[2]	1	1	0.448	0	-0.037	0.032
logSREP_re[3]	1	1	0.142	1	1.096	0.033
logSREP_re[4]	1	1	0.917	1	-0.970	0.032
logSREP_re[5]	1	1	0.448	1	-0.740	0.030
logSREP_re[6]	1	1	0.331	1	0.404	0.035
logSREP_re[7]	1	1	0.391	0	0.162	0.035
logSREP_re[8]	1	1	0.335	1	-1.076	0.044
logSREP_re[9]	1	1	0.426	1	0.724	0.037
logSREP_re[10]	1	1	0.419	1	0.433	0.028
logSREP_re[11]	1	1	0.745	0	-0.372	0.042
logSREP_re[12]	1	1	0.834	1	0.756	0.030
logSREP_re[13]	1	1	0.326	1	-0.471	0.025
logSREP_re[14]	1	1	0.769	1	0.913	0.028
logSREP_re[15]	1	1	0.306	0	0.295	0.032
logSREP_re[16]	1	1	0.346	1	1.599	0.030
logSREP_re[17]	1	1	0.375	0	0.048	0.045
logSREP_re[18]	1	251	0.287	1	-0.756	0.033
logSREP_re[19]	1	1	0.715	1	-0.536	0.032
logSREP_re[20]	1	1	0.125	1	-0.862	0.039
logSREP_re[21]	1	1	0.386	1	0.809	0.032
logSREP_re[22]	1	1	0.505	1	-1.269	0.029
logSREP_re[23]	1	1	0.992	0	0.350	0.036
logSREP_re[24]	1	1	0.402	1	-0.364	0.030
logSREP_re[25]	1	1	0.758	1	-0.536	0.028
logAlpha0	1	1	0.521	1	1.560	0.006
logAlpha_re[1]	1	1	0.824	0	-0.337	0.036
logAlpha_re[2]	1	1	0.617	1	-0.762	0.036
logAlpha_re[3]	0	NA	0.005	NA	NA	NA
logAlpha_re[4]	1	1	0.487	1	-0.359	0.035
logAlpha_re[5]	1	1	0.213	0	0.301	0.032
logAlpha_re[6]	1	1	1.000	1	-0.474	0.034
logAlpha_re[7]	1	1	0.723	0	-0.267	0.031
logAlpha_re[8]	1	1	0.851	0	-0.049	0.042
logAlpha_re[9]	1	1	0.485	1	0.907	0.038
logAlpha_re[10]	1	1	0.507	1	-0.636	0.034
logAlpha_re[11]	1	1	0.054	1	0.435	0.041
logAlpha_re[12]	1	1	0.512	1	0.532	0.030
logAlpha_re[13]	1	1	0.300	0	-0.038	0.031
logAlpha_re[14]	1	1	0.782	1	0.446	0.033
logAlpha_re[15]	1	1	0.292	0	0.361	0.036
logAlpha_re[16]	1	1	0.479	0	-0.052	0.032
logAlpha_re[17]	1	251	0.096	1	0.935	0.035
logAlpha_re[18]	1	1	0.357	1	0.518	0.042
logAlpha_re[19]	1	1	0.116	0	0.192	0.039
logAlpha_re[20]	1	1	0.262	0	-0.286	0.036
logAlpha_re[21]	1	1	0.144	1	0.794	0.034
logAlpha_re[22]	1	1	0.616	1	-0.627	0.037
logAlpha_re[23]	1	1	0.926	0	-0.144	0.034
logAlpha_re[24]	1	1	0.937	0	-0.052	0.037
logAlpha_re[25]	1	1	0.754	0	-0.036	0.032
tauobs[1]	1	1	0.971	1	0.996	0.012
tauobs[2]	1	501	0.061	1	3.306	0.043
tauobs[3]	1	1	0.286	1	3.325	0.039
tauobs[4]	1	1	0.994	1	4.309	0.043
tauobs[5]	1	1	0.230	1	2.543	0.028
tauobs[6]	1	1	0.139	1	4.054	0.044
tauobs[7]	1	1	0.124	1	1.742	0.019
tauobs[8]	1	1	0.333	1	3.124	0.042
tauobs[9]	1	1	0.262	1	4.165	0.049
tauobs[10]	1	1	0.783	1	2.367	0.023
tauobs[11]	1	1	0.424	1	1.811	0.025
tauobs[12]	1	1	0.567	1	5.315	0.054
tauobs[13]	1	1001	0.145	1	5.474	0.073
tauobs[14]	1	1	0.864	1	2.661	0.026
tauobs[15]	1	1	0.745	1	6.427	0.083
tauobs[16]	0	NA	0.006	NA	NA	NA
tauobs[17]	1	1	0.278	1	6.817	0.072
tauobs[18]	1	1	0.978	1	2.223	0.051
tauobs[19]	1	1	0.115	1	1.769	0.030
tauobs[20]	1	1	0.711	1	2.131	0.026
tauobs[21]	1	1	0.543	1	2.761	0.035
tauobs[22]	1	1	0.362	1	3.072	0.040
tauobs[23]	1	1	0.206	1	2.047	0.020
tauobs[24]	1	1	0.990	1	1.392	0.021
tauobs[25]	1	1	0.772	1	1.469	0.023
logSREP_sd	1	1	0.381	1	0.417	0.006
logAlpha_sd	1	1	0.305	1	0.204	0.007
logAlpha02	1	1	0.697	1	0.292	0.009
lp__	1	1	0.253	1	-774.481	0.640

Show Chain 2

	stest	start	pvalue	htest	mean	halfwidth
b0[1]	1	1	0.342	1	8.946	0.010
b0[2]	1	1	0.509	1	1.048	0.015
bWA[1]	1	1	0.324	1	0.682	0.004
bWA[2]	1	1	0.960	1	0.281	0.009
logSREP_re[1]	1	1	0.463	1	0.756	0.038
logSREP_re[2]	1	1	0.490	0	-0.066	0.030
logSREP_re[3]	1	1	0.915	1	1.087	0.030
logSREP_re[4]	1	1	0.233	1	-0.992	0.026
logSREP_re[5]	1	1	0.424	1	-0.770	0.026
logSREP_re[6]	1	1	0.526	1	0.400	0.032
logSREP_re[7]	1	1	0.163	0	0.168	0.032
logSREP_re[8]	1	1	0.493	1	-1.072	0.034
logSREP_re[9]	1	1	0.122	1	0.744	0.031
logSREP_re[10]	1	1	0.527	1	0.410	0.025
logSREP_re[11]	1	1	0.733	1	-0.359	0.036
logSREP_re[12]	1	1	0.158	1	0.744	0.032
logSREP_re[13]	1	1	0.951	1	-0.480	0.025
logSREP_re[14]	1	1	0.250	1	0.915	0.029
logSREP_re[15]	1	1	0.096	0	0.286	0.030
logSREP_re[16]	1	1	0.213	1	1.603	0.029
logSREP_re[17]	1	1	0.808	0	0.024	0.039
logSREP_re[18]	1	1	0.700	1	-0.731	0.027
logSREP_re[19]	1	1	0.980	1	-0.558	0.028
logSREP_re[20]	1	1	0.317	1	-0.842	0.033
logSREP_re[21]	1	1	0.249	1	0.774	0.031
logSREP_re[22]	1	1	0.627	1	-1.275	0.028
logSREP_re[23]	1	1	0.902	1	0.357	0.027
logSREP_re[24]	1	1	0.884	1	-0.388	0.027
logSREP_re[25]	1	1	0.644	1	-0.558	0.024
logAlpha0	1	1	0.343	1	1.559	0.006
logAlpha_re[1]	1	1	0.320	1	-0.335	0.026
logAlpha_re[2]	1	1001	0.061	1	-0.698	0.041
logAlpha_re[3]	1	1	0.980	0	-0.199	0.026
logAlpha_re[4]	1	1	0.975	1	-0.387	0.027
logAlpha_re[5]	1	1	0.941	0	0.279	0.028
logAlpha_re[6]	1	1	0.783	1	-0.491	0.026
logAlpha_re[7]	1	1	0.765	0	-0.234	0.027
logAlpha_re[8]	1	1	0.410	0	-0.064	0.035
logAlpha_re[9]	1	501	0.236	1	0.892	0.035
logAlpha_re[10]	1	1	0.083	1	-0.619	0.027
logAlpha_re[11]	1	1	0.300	1	0.407	0.029
logAlpha_re[12]	1	501	0.161	1	0.536	0.032
logAlpha_re[13]	1	1	0.236	0	-0.046	0.025
logAlpha_re[14]	1	1	0.161	1	0.452	0.027
logAlpha_re[15]	1	1	0.181	1	0.340	0.028
logAlpha_re[16]	1	1	0.128	0	-0.094	0.029
logAlpha_re[17]	1	1	0.394	1	0.928	0.030
logAlpha_re[18]	1	1	0.208	1	0.450	0.031
logAlpha_re[19]	1	1	0.129	0	0.220	0.031
logAlpha_re[20]	1	1	0.879	1	-0.344	0.030
logAlpha_re[21]	1	501	0.054	1	0.804	0.037
logAlpha_re[22]	1	1	0.244	1	-0.699	0.034
logAlpha_re[23]	1	1	0.955	0	-0.166	0.025
logAlpha_re[24]	1	1	0.231	0	-0.056	0.026
logAlpha_re[25]	1	1	0.501	0	-0.011	0.027
tauobs[1]	1	1	0.496	1	0.994	0.010
tauobs[2]	1	1	0.783	1	3.343	0.032
tauobs[3]	1	1	0.528	1	3.306	0.030
tauobs[4]	1	1	0.064	1	4.311	0.042
tauobs[5]	1	1	0.598	1	2.533	0.025
tauobs[6]	1	1	0.921	1	4.054	0.035
tauobs[7]	1	1	0.241	1	1.730	0.015
tauobs[8]	1	1	0.454	1	3.082	0.034
tauobs[9]	1	1	0.097	1	4.191	0.041
tauobs[10]	1	251	0.071	1	2.381	0.019
tauobs[11]	1	1	0.247	1	1.795	0.021
tauobs[12]	1	1	0.381	1	5.367	0.045
tauobs[13]	1	1	0.771	1	5.352	0.046
tauobs[14]	1	1	0.290	1	2.637	0.022
tauobs[15]	1	751	0.056	1	6.385	0.074
tauobs[16]	1	1	0.685	1	4.584	0.053
tauobs[17]	1	1	0.135	1	6.774	0.060
tauobs[18]	1	1	0.817	1	2.191	0.044
tauobs[19]	1	1	0.827	1	1.768	0.026
tauobs[20]	1	1	0.401	1	2.135	0.023
tauobs[21]	1	1	0.491	1	2.779	0.028
tauobs[22]	1	1	0.289	1	3.090	0.034
tauobs[23]	1	1	0.713	1	2.042	0.014
tauobs[24]	1	1	0.071	1	1.371	0.016
tauobs[25]	1	1	0.472	1	1.479	0.020
logSREP_sd	1	1	0.209	1	0.410	0.006
logAlpha_sd	1	1	0.118	1	0.209	0.008
logAlpha02	1	1	0.642	1	0.291	0.009
lp__	1	1	0.080	1	-774.390	0.691

Show Chain 3

	stest	start	pvalue	htest	mean	halfwidth
b0[1]	1	1	0.612	1	8.948	0.011
b0[2]	1	1	0.601	1	1.051	0.015
bWA[1]	1	1	0.453	1	0.683	0.004
bWA[2]	1	1	0.579	1	0.277	0.009
logSREP_re[1]	1	1	0.566	1	0.753	0.033
logSREP_re[2]	1	1	0.641	0	-0.071	0.030
logSREP_re[3]	1	1	0.357	1	1.074	0.031
logSREP_re[4]	1	1	0.868	1	-1.003	0.030
logSREP_re[5]	1	1	0.345	1	-0.768	0.030
logSREP_re[6]	1	1	0.180	1	0.404	0.030
logSREP_re[7]	1	1	0.158	0	0.166	0.032
logSREP_re[8]	1	1	0.140	1	-1.071	0.034
logSREP_re[9]	1	1	0.581	1	0.734	0.034
logSREP_re[10]	1	1	0.277	1	0.414	0.023
logSREP_re[11]	1	1	0.820	1	-0.367	0.036
logSREP_re[12]	1	1	0.662	1	0.737	0.026
logSREP_re[13]	1	1	0.724	1	-0.501	0.021
logSREP_re[14]	1	1	0.191	1	0.899	0.024
logSREP_re[15]	1	1	0.572	0	0.301	0.031
logSREP_re[16]	1	1	0.143	1	1.595	0.028
logSREP_re[17]	1	1	0.736	0	0.011	0.043
logSREP_re[18]	1	1	0.540	1	-0.743	0.030
logSREP_re[19]	1	1	0.415	1	-0.533	0.029
logSREP_re[20]	1	1	0.542	1	-0.838	0.032
logSREP_re[21]	1	1	0.788	1	0.778	0.026
logSREP_re[22]	1	1	0.278	1	-1.291	0.021
logSREP_re[23]	1	1	0.599	1	0.336	0.024
logSREP_re[24]	1	1	0.378	1	-0.391	0.025
logSREP_re[25]	1	1	0.282	1	-0.549	0.025
logAlpha0	1	1	0.362	1	1.557	0.006
logAlpha_re[1]	1	1	0.104	1	-0.331	0.028
logAlpha_re[2]	1	1	0.229	1	-0.735	0.032
logAlpha_re[3]	1	1	0.468	0	-0.189	0.026
logAlpha_re[4]	1	1	0.273	1	-0.364	0.027
logAlpha_re[5]	1	1	0.082	1	0.280	0.027
logAlpha_re[6]	1	1	0.700	1	-0.491	0.027
logAlpha_re[7]	1	1	0.295	0	-0.213	0.025
logAlpha_re[8]	1	1	0.679	0	-0.047	0.033
logAlpha_re[9]	1	1	0.153	1	0.905	0.033
logAlpha_re[10]	1	1	0.580	1	-0.621	0.026
logAlpha_re[11]	1	1	0.502	1	0.385	0.029
logAlpha_re[12]	1	1	0.793	1	0.566	0.028
logAlpha_re[13]	1	1	0.843	0	-0.031	0.025
logAlpha_re[14]	1	1	0.659	1	0.473	0.025
logAlpha_re[15]	1	1	0.203	1	0.342	0.028
logAlpha_re[16]	1	1	0.187	0	-0.061	0.026
logAlpha_re[17]	1	1	0.467	1	0.939	0.033
logAlpha_re[18]	1	1	0.858	1	0.483	0.032
logAlpha_re[19]	1	1	0.852	0	0.170	0.026
logAlpha_re[20]	1	1	0.390	1	-0.335	0.028
logAlpha_re[21]	1	1	0.726	1	0.792	0.032
logAlpha_re[22]	1	1	0.096	1	-0.666	0.032
logAlpha_re[23]	1	1	0.516	0	-0.165	0.026
logAlpha_re[24]	1	1	0.954	0	-0.039	0.025
logAlpha_re[25]	1	1	0.598	0	-0.027	0.026
tauobs[1]	1	1	0.957	1	0.994	0.010
tauobs[2]	1	1	0.845	1	3.324	0.032
tauobs[3]	1	1	0.216	1	3.302	0.030
tauobs[4]	1	1	0.403	1	4.353	0.039
tauobs[5]	1	1	0.389	1	2.538	0.023
tauobs[6]	1	1	0.335	1	4.033	0.036
tauobs[7]	1	251	0.249	1	1.721	0.015
tauobs[8]	1	1	0.830	1	3.127	0.034
tauobs[9]	1	1	0.875	1	4.155	0.038
tauobs[10]	1	251	0.065	1	2.383	0.021
tauobs[11]	1	1	0.724	1	1.772	0.018
tauobs[12]	1	1	0.102	1	5.338	0.045
tauobs[13]	1	1	0.797	1	5.424	0.042
tauobs[14]	1	1	0.973	1	2.660	0.020
tauobs[15]	1	1	0.281	1	6.486	0.063
tauobs[16]	1	1	0.323	1	4.568	0.047
tauobs[17]	1	1	0.172	1	6.783	0.052
tauobs[18]	1	1	0.953	1	2.192	0.042
tauobs[19]	0	NA	0.007	NA	NA	NA
tauobs[20]	1	1	0.603	1	2.136	0.019
tauobs[21]	1	1	0.588	1	2.750	0.026
tauobs[22]	1	501	0.276	1	3.109	0.033
tauobs[23]	1	1	0.103	1	2.054	0.015
tauobs[24]	1	1	0.826	1	1.385	0.015
tauobs[25]	1	1	0.421	1	1.454	0.019
logSREP_sd	1	1	0.827	1	0.413	0.007
logAlpha_sd	1	1	0.510	1	0.205	0.007
logAlpha02	1	1	0.334	1	0.291	0.008
lp__	1	1	0.910	1	-774.671	0.675

Show Chain 4

	stest	start	pvalue	htest	mean	halfwidth
b0[1]	1	1	0.557	1	8.956	0.012
b0[2]	1	1	0.821	1	1.048	0.015
bWA[1]	1	1	0.634	1	0.679	0.004
bWA[2]	1	1	0.569	1	0.284	0.011
logSREP_re[1]	1	1	0.494	1	0.730	0.044
logSREP_re[2]	1	1	0.190	0	-0.077	0.032
logSREP_re[3]	1	1	0.532	1	1.097	0.034
logSREP_re[4]	1	751	0.207	1	-1.041	0.039
logSREP_re[5]	1	1	0.173	1	-0.790	0.031
logSREP_re[6]	1	1	0.880	1	0.381	0.037
logSREP_re[7]	1	1	0.487	0	0.134	0.037
logSREP_re[8]	1	1	0.766	1	-1.031	0.048
logSREP_re[9]	1	1	0.513	1	0.697	0.039
logSREP_re[10]	1	1	0.961	1	0.408	0.028
logSREP_re[11]	1	1	0.841	0	-0.353	0.043
logSREP_re[12]	1	1	0.677	1	0.732	0.033
logSREP_re[13]	1	1	0.378	1	-0.526	0.030
logSREP_re[14]	1	1	0.838	1	0.901	0.030
logSREP_re[15]	1	1	0.845	0	0.267	0.034
logSREP_re[16]	1	1	0.814	1	1.595	0.026
logSREP_re[17]	1	1	0.657	0	0.039	0.046
logSREP_re[18]	1	1	0.478	1	-0.715	0.032
logSREP_re[19]	1	1	0.779	1	-0.539	0.035
logSREP_re[20]	1	501	0.082	1	-0.789	0.044
logSREP_re[21]	1	1	0.841	1	0.787	0.034
logSREP_re[22]	1	1	0.487	1	-1.306	0.034
logSREP_re[23]	1	1	0.924	0	0.319	0.038
logSREP_re[24]	1	1	0.982	1	-0.392	0.034
logSREP_re[25]	1	1	0.750	1	-0.598	0.030
logAlpha0	1	1	0.172	1	1.556	0.007
logAlpha_re[1]	1	1	0.694	0	-0.313	0.034
logAlpha_re[2]	1	1	0.342	1	-0.729	0.037
logAlpha_re[3]	1	1	0.318	0	-0.196	0.033
logAlpha_re[4]	1	1	0.868	1	-0.371	0.036
logAlpha_re[5]	1	1	0.579	0	0.295	0.036
logAlpha_re[6]	1	1	0.630	1	-0.515	0.034
logAlpha_re[7]	1	1	0.644	0	-0.243	0.035
logAlpha_re[8]	1	1	0.712	0	-0.092	0.041
logAlpha_re[9]	1	1	0.462	1	0.924	0.037
logAlpha_re[10]	1	1	0.217	1	-0.613	0.038
logAlpha_re[11]	1	1	0.728	0	0.384	0.045
logAlpha_re[12]	1	1	0.080	1	0.566	0.032
logAlpha_re[13]	1	1	0.463	0	-0.011	0.033
logAlpha_re[14]	1	1	0.345	1	0.491	0.035
logAlpha_re[15]	1	1	0.105	0	0.355	0.038
logAlpha_re[16]	1	1	0.145	0	-0.069	0.030
logAlpha_re[17]	1	1	0.812	1	0.930	0.038
logAlpha_re[18]	1	1	0.411	1	0.472	0.040
logAlpha_re[19]	1	1	0.074	0	0.197	0.036
logAlpha_re[20]	1	1	0.109	0	-0.334	0.040
logAlpha_re[21]	1	1	0.719	1	0.788	0.038
logAlpha_re[22]	1	1	0.777	1	-0.702	0.038
logAlpha_re[23]	1	1	0.336	0	-0.151	0.036
logAlpha_re[24]	1	1	0.685	0	-0.029	0.036
logAlpha_re[25]	1	1	0.740	0	-0.020	0.036
tauobs[1]	1	1	0.844	1	1.002	0.014
tauobs[2]	1	1	0.579	1	3.321	0.037
tauobs[3]	1	1	0.702	1	3.305	0.039
tauobs[4]	1	1	0.531	1	4.364	0.049
tauobs[5]	1	1	0.082	1	2.569	0.031
tauobs[6]	1	1	0.495	1	4.033	0.049
tauobs[7]	1	1	0.784	1	1.725	0.021
tauobs[8]	1	1	0.909	1	3.040	0.043
tauobs[9]	1	1	0.725	1	4.163	0.043
tauobs[10]	1	1	0.758	1	2.375	0.022
tauobs[11]	1	1	0.388	1	1.768	0.022
tauobs[12]	1	1	0.737	1	5.341	0.058
tauobs[13]	1	1	0.817	1	5.397	0.059
tauobs[14]	1	1	0.866	1	2.648	0.029
tauobs[15]	1	1	0.647	1	6.407	0.083
tauobs[16]	1	1	0.773	1	4.524	0.065
tauobs[17]	1	1	0.569	1	6.694	0.069
tauobs[18]	1	1	0.647	1	2.150	0.053
tauobs[19]	1	1	0.552	1	1.749	0.033
tauobs[20]	1	1001	0.054	1	2.107	0.032
tauobs[21]	1	1	0.701	1	2.734	0.037
tauobs[22]	1	1	0.338	1	3.073	0.042
tauobs[23]	1	1	0.441	1	2.050	0.021
tauobs[24]	1	1	0.931	1	1.398	0.021
tauobs[25]	1	1	0.206	1	1.458	0.024
logSREP_sd	1	1	0.674	1	0.406	0.007
logAlpha_sd	1	1	0.192	1	0.209	0.007
logAlpha02	1	1	0.597	1	0.291	0.011
lp__	1	1	0.711	1	-775.272	0.649

Effective Sample Size

Show table

Parameter	EffectiveSize
b0[1]	2597.1
b0[2]	3107.5
bWA[1]	3646.1
bWA[2]	4274.1
logSREP_re[1]	5841.1
logSREP_re[2]	4046.5
logSREP_re[3]	4606.6
logSREP_re[4]	4578.9
logSREP_re[5]	5465.3
logSREP_re[6]	3613.4
logSREP_re[7]	3906.9
logSREP_re[8]	8284.0
logSREP_re[9]	4013.4
logSREP_re[10]	6704.3
logSREP_re[11]	6140.6
logSREP_re[12]	5289.2
logSREP_re[13]	5343.3
logSREP_re[14]	4455.1
logSREP_re[15]	3346.5
logSREP_re[16]	4431.9
logSREP_re[17]	3938.6
logSREP_re[18]	6651.0
logSREP_re[19]	7425.7
logSREP_re[20]	9238.4
logSREP_re[21]	7281.3
logSREP_re[22]	6692.6
logSREP_re[23]	10771.4
logSREP_re[24]	8050.0
logSREP_re[25]	8184.4
logAlpha0	4701.1
logAlpha_re[1]	15022.2
logAlpha_re[2]	10156.7
logAlpha_re[3]	13114.8
logAlpha_re[4]	12007.7
logAlpha_re[5]	11322.7
logAlpha_re[6]	11220.6
logAlpha_re[7]	12325.0
logAlpha_re[8]	8358.0
logAlpha_re[9]	8535.2
logAlpha_re[10]	9648.9
logAlpha_re[11]	12098.3
logAlpha_re[12]	10076.9
logAlpha_re[13]	11395.0
logAlpha_re[14]	12722.8
logAlpha_re[15]	13159.5
logAlpha_re[16]	14233.1
logAlpha_re[17]	8131.8
logAlpha_re[18]	11305.8
logAlpha_re[19]	13282.9
logAlpha_re[20]	10188.9
logAlpha_re[21]	9335.9
logAlpha_re[22]	10219.0
logAlpha_re[23]	10970.9
logAlpha_re[24]	15444.5
logAlpha_re[25]	15986.5
tauobs[1]	17575.5
tauobs[2]	13912.5
tauobs[3]	16397.0
tauobs[4]	15259.9
tauobs[5]	13875.1
tauobs[6]	15905.8
tauobs[7]	15872.5
tauobs[8]	11998.5
tauobs[9]	13559.6
tauobs[10]	16464.7
tauobs[11]	14120.5
tauobs[12]	15229.9
tauobs[13]	15306.8
tauobs[14]	15489.2
tauobs[15]	15856.1
tauobs[16]	16601.8
tauobs[17]	13658.5
tauobs[18]	9992.6
tauobs[19]	14112.2
tauobs[20]	14742.4
tauobs[21]	14751.4
tauobs[22]	14587.1
tauobs[23]	16304.2
tauobs[24]	14263.8
tauobs[25]	14523.4
logSREP_sd	3112.5
logAlpha_sd	2562.9
logAlpha02	4734.1
lp__	2428.7

Gelman Statistic

Show table

Parameter	Point est.	Upper C.I.
b0[1]	1.001	1.004
b0[2]	1.000	1.000
bWA[1]	1.001	1.002
bWA[2]	1.000	1.001
logSREP_re[1]	1.000	1.000
logSREP_re[2]	1.001	1.002
logSREP_re[3]	1.000	1.001
logSREP_re[4]	1.001	1.003
logSREP_re[5]	1.001	1.003
logSREP_re[6]	1.000	1.001
logSREP_re[7]	1.001	1.002
logSREP_re[8]	1.000	1.001
logSREP_re[9]	1.001	1.002
logSREP_re[10]	1.000	1.001
logSREP_re[11]	1.000	1.000
logSREP_re[12]	1.000	1.001
logSREP_re[13]	1.002	1.006
logSREP_re[14]	1.000	1.001
logSREP_re[15]	1.001	1.002
logSREP_re[16]	1.000	1.000
logSREP_re[17]	1.000	1.001
logSREP_re[18]	1.001	1.001
logSREP_re[19]	1.000	1.000
logSREP_re[20]	1.001	1.001
logSREP_re[21]	1.000	1.001
logSREP_re[22]	1.001	1.002
logSREP_re[23]	1.001	1.001
logSREP_re[24]	1.000	1.001
logSREP_re[25]	1.001	1.004
logAlpha0	1.000	1.001
logAlpha_re[1]	1.000	1.000
logAlpha_re[2]	1.000	1.000
logAlpha_re[3]	1.000	1.000
logAlpha_re[4]	1.000	1.000
logAlpha_re[5]	1.000	1.000
logAlpha_re[6]	1.000	1.001
logAlpha_re[7]	1.001	1.002
logAlpha_re[8]	1.000	1.001
logAlpha_re[9]	1.000	1.000
logAlpha_re[10]	1.000	1.001
logAlpha_re[11]	1.000	1.001
logAlpha_re[12]	1.000	1.001
logAlpha_re[13]	1.000	1.001
logAlpha_re[14]	1.001	1.001
logAlpha_re[15]	1.000	1.000
logAlpha_re[16]	1.000	1.001
logAlpha_re[17]	1.000	1.000
logAlpha_re[18]	1.001	1.002
logAlpha_re[19]	1.000	1.001
logAlpha_re[20]	1.001	1.002
logAlpha_re[21]	1.000	1.000
logAlpha_re[22]	1.001	1.003
logAlpha_re[23]	1.000	1.000
logAlpha_re[24]	1.000	1.000
logAlpha_re[25]	1.000	1.000
tauobs[1]	1.000	1.001
tauobs[2]	1.000	1.000
tauobs[3]	1.000	1.000
tauobs[4]	1.001	1.001
tauobs[5]	1.000	1.001
tauobs[6]	1.000	1.000
tauobs[7]	1.001	1.001
tauobs[8]	1.001	1.003
tauobs[9]	1.000	1.000
tauobs[10]	1.000	1.000
tauobs[11]	1.001	1.002
tauobs[12]	1.000	1.000
tauobs[13]	1.000	1.001
tauobs[14]	1.000	1.000
tauobs[15]	1.000	1.000
tauobs[16]	1.000	1.001
tauobs[17]	1.000	1.001
tauobs[18]	1.000	1.001
tauobs[19]	1.000	1.000
tauobs[20]	1.000	1.000
tauobs[21]	1.000	1.001
tauobs[22]	1.000	1.000
tauobs[23]	1.000	1.000
tauobs[24]	1.001	1.001
tauobs[25]	1.000	1.001
logSREP_sd	1.003	1.007
logAlpha_sd	1.001	1.002
logAlpha02	1.000	1.000
lp__	1.001	1.004

5. Prior Predictive Plots

Show figure

6. SR Curves

Show figure: Spawner-Recruit Curves

7. Posterior Residual Plots

Posterior P-Values of logRS Residuals

Show figure: Posterior P-Value for logRS

Where the posterior p-value represents the proportion of simulated means above the observed mean. In this case a value of 0.5414, which indicates a slightly higher bias of the simulated responses over the observations.

Posterior Distribution of logSREP residuals against WA and latitude

Show figure: Residuals of logSREP_re: Ocean Type

Show figure: Residuals of logSREP_re: Stream Type

Residuals of Posterior Predictive against Years and Observed Spawners

Show figure: Residuals of logRS by Year

Show figure: Residuals of logRS by Spawners

Q-Q Norm Plot of Residuals

Show figure: QQNorm Plot of logRS

8. Residual Autocorrelation Plots

Show figure: Residuals ACF of Spawner-Recruit Relationship